Mathematics Algebraic Geometry From Rs Cy Dimension Eq D

The Calabi-Yau dimension

A Calabi-Yau threefold is a compact six-dimensional shape that satisfies the vacuum Einstein equations in string theory, leaving one quarter of the supersymmetry unbroken. Its complex dimension is 3, which is the D in the declaration's name. The Recognition Science (RS) framework, which builds structure from a discrete record of recognition events, defines a constant called configDim, the configuration dimension, and proves that this constant equals 3.

The theorem cyDimension_eq_D states that the framework's own definition of a Calabi-Yau threefold dimension, cyDimension, is definitionally equal to 3. This is a formal identity, checked by the machine: the declaration is a theorem in the framework's machine-checked library of formal theorems, with no unproved assumptions. The certificate structure bundles this identity with the count of five canonical algebraic geometry objects, providing a single formal object that records both facts.

The declaration does not claim that the physical universe is a Calabi-Yau threefold, nor that the framework has derived the mirror symmetry of such a shape. It only establishes a numerical coincidence within the framework's own definitions: the configuration dimension, which counts five canonical algebraic geometry objects, equals the complex dimension of a Calabi-Yau threefold. The physical bridge, from the recognition ledger to the geometry of spacetime, remains an open target.

theorem cyDimension_eq_D : cyDimension = 3 := rfl

def algebraicGeometryCert : AlgebraicGeometryCert where
  five_objects := agObjectCount
  cy_dim := cyDimension_eq_D

What this page does not claim

The declaration does not prove that the physical universe is a Calabi-Yau threefold. The declaration does not derive the mirror symmetry of a Calabi-Yau threefold. The declaration does not establish the physical bridge from the recognition ledger to spacetime geometry.

Verify this page

Every tagged claim above names its theorem. To check one yourself rather than trust this page, elaborate the source module with Lean 4 and audit its axiom basis:

$ lake env lean IndisputableMonolith/Mathematics/AlgebraicGeometryFromRS.lean
expected axiom basis: [propext, Classical.choice, Quot.sound] (the Lean kernel's standard three; no RS-specific axioms)

A page whose claims cannot be reproduced this way does not ship. In production, every anchor links to the exact declaration in the public source release, and this block carries the build receipt for the page itself.

Derived articles

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